Tour HDU - 3488

Posted 2020-10-21 yijiull

Tour

 HDU - 3488 

可以用费用流做 

  1 #include <bits/stdc++.h>
  2 using namespace std;
  3 const int inf = 0x3f3f3f3f;
  4 const int maxv = 410;
  5 const int maxe = maxv * maxv;
  6 
  7 struct Edge{
  8     int u, v, cap, flow, cost;
  9     int nxt;
 10     Edge(int u = 0, int v = 0, int cap = 0, int flow = 0, int cost = 0, int nxt = 0) : 
 11         u(u), v(v), cap(cap), flow(flow), cost(cost), nxt(nxt) {}
 12 }e[maxe << 1];
 13 
 14 int head[maxv];
 15 int cnt;
 16 void init(){
 17     cnt = 0;
 18     memset(head, -1, sizeof head);
 19 }
 20 
 21 void add(int u, int v, int cap, int cost){
 22     e[cnt] = Edge(u, v, cap, 0, cost, head[u]);
 23     head[u] = cnt++;
 24     e[cnt] = Edge(v, u, 0, 0, -cost, head[v]);
 25     head[v] = cnt++;
 26 }
 27 
 28 int N;
 29 int d[maxv], p[maxv], a[maxv], inq[maxv];
 30 bool BellmanFord(int s, int t, int &flow, int &cost){
 31     for(int i = 0; i < N; i++) d[i] = inf;
 32     memset(inq, 0, sizeof inq);
 33     d[s] = 0, a[s] = inf, p[s] = 0, inq[s] = 1;
 34     queue<int> q;
 35     q.push(s);
 36     while(!q.empty()){
 37         int u = q.front();
 38         q.pop();
 39         inq[u] = 0;
 40         for(int i = head[u]; ~i; i = e[i].nxt){
 41             Edge &tp = e[i];
 42             if(tp.cap > tp.flow && d[tp.v] > d[u] + tp.cost){
 43                 d[tp.v] = d[u] + tp.cost;
 44                 p[tp.v] = i;
 45                 a[tp.v] = min(a[u], tp.cap - tp.flow);
 46                 if(!inq[tp.v]){
 47                     q.push(tp.v);
 48                     inq[tp.v] = 1;
 49                 }
 50             }
 51         }
 52     }
 53     if(d[t] == inf) return false;
 54     flow += a[t];
 55     cost += a[t] * d[t];
 56     int u = t;
 57     while(u != s){
 58         e[p[u]].flow += a[t];
 59         e[p[u] ^ 1].flow -= a[t];
 60         u = e[p[u]].u;
 61     }
 62     return true;
 63 }
 64 
 65 
 66 int MCMF(int s, int t){
 67     int flow = 0, cost = 0;
 68     while(BellmanFord(s, t, flow, cost));
 69     return cost;
 70 }
 71 
 72 int gra[maxv<<1][maxv<<1];
 73 int main(){
 74     int t;
 75     scanf("%d", &t);
 76     while(t--){
 77         memset(gra, inf, sizeof(gra));
 78         init();
 79         int n, m;
 80         scanf("%d %d", &n, &m);
 81         int u, v, w;
 82         for(int i = 0; i < m; i++){
 83             scanf("%d %d %d", &u, &v, &w);
 84             gra[u * 2 + 1][v * 2] = min(gra[u * 2 + 1][v * 2], w);
 85         }
 86         for(int i = 2; i <= n * 2 + 1; i++){
 87             for(int j = 2; j <= n * 2 + 1; j++){
 88                 if(gra[i][j] != inf) add(i, j, 1, gra[i][j]);
 89             }
 90         }
 91         int S = 0, T = 1;
 92         N = 2 * n + 2;
 93         for(int i = 1; i <= n; i++){
 94             add(S, i * 2 + 1, 1, 0);
 95             add(i * 2, T, 1, 0);
 96         }
 97         printf("%d\n", MCMF(S, T));
 98     }
 99     return 0;
100 }

View Code

 

也可以用KM

 1 #include <bits/stdc++.h>
 2 using namespace std;
 3 const int maxv=210;
 4 const int inf=0x3f3f3f3f;
 5 
 6 int vb[maxv],vg[maxv],eb[maxv],eg[maxv];
 7 int c[maxv][maxv];
 8 int slack[maxv];
 9 int mc[maxv];
10 #define CLR(m,a) memset(m,a,sizeof(m))
11 int n,m;
12 int dfs(int x)
13 {
14     vg[x]=1;
15     for(int i=0;i<n;i++)
16     {
17         if(vb[i]) continue;
18         int gap=eg[x]+eb[i]-c[x][i];
19         if(gap==0)
20         {
21             vb[i]=1;
22             if(mc[i]==-1||dfs(mc[i]))
23             {
24                 mc[i]=x;
25                 return 1;
26             }
27         }
28         else slack[i]=min(slack[i],gap);
29     }
30     return 0;
31 }
32 int KM()
33 {
34     CLR(mc,-1);
35     CLR(eb,0);
36     for(int i=0;i<n;i++)
37     {
38         eg[i]=c[i][0];
39         for(int j=1;j<n;j++)
40             eg[i]=max(eg[i],c[i][j]);
41     }
42     for(int i=0;i<n;i++)
43     {
44         CLR(slack,inf);
45         while(1)
46         {
47             CLR(vb,0);
48             CLR(vg,0);
49             if(dfs(i)) break;
50             int d=inf;
51             for(int i=0;i<n;i++) if(!vb[i]) d=min(d,slack[i]);
52             for(int i=0;i<n;i++)
53             {
54                 if(vg[i]) eg[i]-=d;
55                 if(vb[i]) eb[i]+=d;
56                 else slack[i]-=d;
57             }
58         }
59     }
60     int ans=0;
61     for(int i=0;i<n;i++)
62     {
63         if(mc[i]==-1) return -1;
64         if(c[mc[i]][i]==-inf) return -1;
65         ans+=c[mc[i]][i];
66     }
67     return -ans;
68 }
69 int main()
70 {
71     int t;
72     scanf("%d",&t);
73     while(t--)
74     {
75         scanf("%d%d",&n,&m);
76         int u,v,w;
77        for(int i=0;i<n;i++)
78         for(int j=0;j<n;j++) c[i][j]=-inf;
79         for(int i=0;i<m;i++)
80         {
81             scanf("%d%d%d",&u,&v,&w);
82             u--;v--;
83             c[u][v]=max(-w,c[u][v]);
84         }
85         printf("%d\n",KM());
86     }
87 }

View Code

 

不同的是建图的时候的区别，费用流要拆点，而KM不用，因为KM左右两边的点已经视为不同了。

这个题还要注意有重边，费用流盲目建图会TLE。